Evaluate : ( 55 -15 ) x [10 + 32 + { 8 – 1 + 3 }].
For 6th grade simple please!!!
Answers
Answer:
2080
Step-by-step explanation:
( 55 -15 ) x [10 + 32 + { 8 – 1 + 3 }]
datos:
(55-15)=40
{ 8 – 1 + 3 }=10
resolución:
( 55 -15 ) x [10 + 32 + { 8 – 1 + 3 }]
40 x [10 + 32 + {10 }]
sumamos la parte del corchete: [10 + 32 + {10 }]=52
40 x [10 + 32 + {10 }]
40 x 52=2080
Related Questions
NO LINKS!! State the Domain and Range for each graph
Answers
Both end points are represented by closed circles, it means both points are included.
The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.
Domain, the set of possible x- coordinates:
x ∈ [- 2, 6]Range, the set of possible y- coordinates:
y ∈ [- 3, 7]The graph on the rightBoth end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.
It makes x-values infinite but y-values restricted between the two lines.
Domain, the set of possible x- coordinates:
x ∈ (- ∞, + ∞)Range, the set of possible y- coordinates:
y ∈ [1, 5]Answer:
1. Domain: [-2, 6]
Range: [-3, 7]
2. Domain: (-∞, ∞)
Range: [1, 5]
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1The domain of the function is restricted since the curve has two distince endpoints. As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.
Domain: [-2, 6]The function has a maximum point at (-1, 7) and a minimum point at (6, -3).
Therefore, the range of the function is restricted.
Range: [-3, 7]Question 2As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.
Domain: (-∞, ∞)The maximum y-value is y = 5. When x < 1, the line continues indefinitely at y = 5.
The minimum value is y = 1. When x > 1, the line continues indefinitely at y = 1.
Therefore, the range of the function is restricted.
Range: [1, 5]In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
Answers
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
For similar question on length.
https://brainly.com/question/30582409
#SPJ8
Solve the system of linear equations by graphing. Round the solution to the nearest tenth as needed.
y + 2.3 = 0.45x
–2y = 4.2x – 7.8
Answers
Answer:
(2.4, -1.2)
Step-by-step explanation:
Answer:
1: (2.4,-1.2)
Step-by-step explanation:
Javier bought a painting for
$
150
$150dollar sign, 150. Each year, the painting's value increases by a factor of
1.15
1.151, point, 15.
Which expression gives the painting's value after
7
77 years?
Choose 1 answer:
Choose 1 answer:
(Choice A)
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
A
(
150
⋅
1.15
)
7
(150⋅1.15)
7
left parenthesis, 150, dot, 1, point, 15, right parenthesis, start superscript, 7, end superscript
(Choice B)
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
B
150
⋅
1.1
5
7
150⋅1.15
7
150, dot, 1, point, 15, start superscript, 7, end superscript
(Choice C)
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
C
(
150
+
1.15
)
⋅
7
(150+1.15)⋅7left parenthesis, 150, plus, 1, point, 15, right parenthesis, dot, 7
(Choice D)
150
+
1.15
⋅
7
150+1.15⋅7150, plus, 1, point, 15, dot, 7
D
150
+
1.15
⋅
7
150+1.15⋅7
Answers
The correct expression is \($(150 \cdot 1.15)^7$\) (Choice A).
The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).
To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.
If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.
Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.
For such more questions on expression
https://brainly.com/question/1859113
#SPJ8
k(k + 1)(k + 2) – 3k(k + 1)
Need a step-by-step guide on how to factor this completely
Answers
Answer:
Step-by-step explanation:
k(k+1)(k+2) - 3k(k+1)
k and (k+1) are common to both terms.
k(k+1)(k+2) - 3k(k+1) = k(k+1)[(k+2) - 3] = k(k+1)(k-1)
Your family needs to rent a car for a week while on
vacation. Company A charges $3.25 per mile plus a flat
fee of $125 per week. Company B charges $3 per mile
plus a flat fee of $150 per week.
A. Write an equation to express the situation
B. After how many miles of travel are the total costs
the same at both companies?
Answers
The equation to represent the situation are as follows:
Company A;
y = 3.25x + 125
Company B;
y = 3x + 150
The miles of travel the total cost will be the same is 100 miles.
How to find the equation that represent the situation?Your family needs to rent a car for a week while on vacation. Company A charges $3.25 per mile plus a flat fee of $125 per week. Company B charges $3 per mile plus a flat fee of $150 per week.
Therefore, the equation to express the situation is as follows;
Company A;
y = 3.25x + 125
Company B;
y = 3x + 150
where
x = number of milesy = total costThe number of miles the travel will cost the same can be calculated as follows:
3.25x + 125 = 3x + 150
3.25x - 3x = 150 - 125
0.25x = 25
x = 25 / 0.25
x = 100
Therefore, the number of miles is 100 miles.
learn more on equation here: https://brainly.com/question/13439238
#SPJ1
The graph of the function rule that models the volume of the sphere has symmetry with respect to ____?
Answers
The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.
Explain the term symmetry along origin?About the Origin: Symmetry. If a point appears on a graph at every time, then the graph is symmetric having respect to the origin. When seen in relation to the origin, this graph is symmetric.A function having a single term which is the sum of a real number, the coefficient, as well as a variable raised to something like a fixed real number is called a power function. (A coefficient is a number which multiplies a variable by an exponent.) Think of equations like area or volume as an illustration.For the stated question.
The volume of the sphere is modeled by the power function with respect to the radius as;
V = f(r) = 4/3πr³
As, r is independent of any of the coordinate axis.
Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.
To know more about the symmetry along origin, here
https://brainly.com/question/1413522
#SPJ1
a/b - c + d if a = 7/8, b= -7/16, c= 0.8 and d= 1/4 write your answer as a mixed number in simplest form? help me please
Answers
a/b - c + d = (7/8) / (-7/16) - 0.8 + 1/4
We can simplify the first term by dividing the numerator by the denominator and multiplying by the reciprocal:
(7/8) / (-7/16) = (7/8) * (-16/7) = -2
Substituting this value, along with the values of c and d, we get:
a/b - c + d = -2 - 0.8 + 1/4
Combining the constant terms, we get:
a/b - c + d = -2.8 + 1/4
To express this as a mixed number in simplest form, we first convert the decimal to a fraction by multiplying both the numerator and denominator by 100:
-2.8 + 1/4 = -280/100 + 25/100
Combining these fractions, we get:
-280/100 + 25/100 = -255/100
To express this as a mixed number, we divide the numerator by the denominator to get the whole number part, and express the remainder as a fraction of the denominator:
-255/100 = -2 55/100 = -2 11/20
Therefore, the answer in mixed number form is -2 11/20.
HELP PLEASE FAST
I’ll get in trouble if I fail and this is already almost due
Answers
What are the domain and range of the function ? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Answers
Answer:
Option A Domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Step-by-step explanation:
Domain corresponds to the values of x and Range corresponds to the value of y. If sketch the graph on an online calculator we can see that the domain lies between -2.5 and 2.5 for x and the range corresponds to y as in this case
range ≥ -5.
Answer:
a
Step-by-step explanation:
The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answers
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
\((-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\\)
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
\((-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\\)
\(= \frac{3440}{160}\)
= $21.5
b. Now The maximum profit could be determined by the following equation
\(f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\\)
= $980
c. The price that would enable the company to break even that is
f(p) = 0
\(f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0\)
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
A bus covers a certain distanc in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to reduce the time by 20 minutes .
Answers
2.66 is the speed
..................................................................................................................................................................................................................................................................................................................................................................................................................................
Brendan says that when a rectangle with length 6 cm and width 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled. Explain what is incorrect about Brendan’s statement.
Answers
The area of a rectangle does double when dilated by a scale factor of 2, the Perimeter does not double. It increases by a factor of 2.
Brendan's statement that when a rectangle with a length of 6 cm and a width of 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled is incorrect. While the area of the rectangle does indeed increase by a factor of 2 when dilated, the perimeter does not necessarily double.
Brendan's statement and understand the concept of dilation:
1. Perimeter: The perimeter of a rectangle is the sum of all its sides. In this case, the original rectangle has a length of 6 cm and a width of 4 cm, resulting in a perimeter of 2*(6 cm + 4 cm) = 20 cm. If we dilate this rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The perimeter of the new rectangle is 2*(12 cm + 8 cm) = 40 cm. As we can see, the perimeter has not doubled; it has increased by a factor of 2.
2. Area: The area of a rectangle is calculated by multiplying its length by its width. For the original rectangle with a length of 6 cm and a width of 4 cm, the area is 6 cm * 4 cm = 24 cm². When we dilate the rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The area of the new rectangle is 12 cm * 8 cm = 96 cm². The area has indeed doubled, as Brendan mentioned.
Therefore, while the area of a rectangle does double when dilated by a scale factor of 2, the perimeter does not double. It increases by a factor of 2. It is crucial to differentiate between the effects of dilation on the area and the perimeter of a shape to have a clear understanding of geometric transformations.
For more questions on Perimeter .
https://brainly.com/question/397857
#SPJ8
if x varies direcly as y and x=9 when y=3 find x when y=12
Answers
Answer:
36
Step-by-step explanation:
x = 9 and y = 3
3 times 3 equal 9 so if y is 12 then 12 x 3 = 36
you want to reach $3,000 in savings over four years your account will earn 10% interest per year how much must you save each month
Answers
You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.
To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate, we can use the PMT (Payment) function.
The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.
Let's break down the given information:
Present Value (PV): $0.00 (initial account balance)
Future Value (FV): $3,000.00 (savings goal)
Interest Rate (rate): 10% per year (annual interest rate)
Number of Periods (nper): 4 years (48 months)
Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).
The formula for the PMT function is:
PMT(rate, nper, pv, [fv], [type])
Where:
rate = Interest rate per period
nper = Total number of periods
pv = Present value (initial account balance)
fv = Future value (savings goal)
type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.
We'll assume 0 for monthly savings.
Let's calculate the monthly savings using the PMT function:
PMT(10%/12, 4*12, 0, -3000, 0)
Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).
Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.
Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.
For similar question on annual interest rate.
https://brainly.com/question/29059795
#SPJ11
Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.
Citizen Bank sent a bank statement to Bane Co. showing an ending balance of $ 1,480. On the bank statement there was a service charge of $20. The bookkeeper of Bane Co. noticed in the reconciliation process a deposit in transit of $200 along with checks outstanding of $300. Complete the reconciliation for Bane assuming a beginning balance of $1,400.
Answers
The reconciliation for Bane can be summarized as,
Adjusted bank balance = $1380.
What is meant by bank Reconciliation?A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.
Given that,
Beginning checkbook balance is $1400.
Service charge = $20
Adjusted balance = $1400 - $20 = $1380
Also, given that,
Ending balance on the statement = $1480
Deposit in transit = $200
Checks outstanding = $300
Adjusted balance = $1480 + 200 - 300
= $1380
Hence the adjusted balance is $1380.
Learn more about Bank Reconciliation here :
https://brainly.com/question/29097188
#SPJ1
Find the value of z such that 0.05 of the area lies to the right of z. Round your answer to two decimal places.
Answers
Answer:
\(z = 1.6\)
Step-by-step explanation:
Given
\(Pr = 0.05\)
Required
The z value to the right
The z value to the right is represented as:
\(P(Z > z)\)
So, the probability is represented as:
\(P(Z > z) = 0.05\)
From z table, the z value that satisfies the above probability is:
\(z = 1.645\)
\(z = 1.6\) --- approximated
Johnny made 8 benches in 2 hours. At this rate, how
many benches will he make in 9 hours.
plzzzzzzzzzz!!!!!!!! help on thissss
Answers
Answer:
36
Step-by-step explanation:
4 benches in 1 hour
? benches in 9 hours
36 benches
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
36 is the answer :)
Step-by-step explanation:
Answering questions for you to help me please
Answers
Answer:
3) 49*x^2*y^2
4) x
5) 1
6) 8
Step-by-step explanation:
3). ( 7xy)^2
=. 7^2 * x^2 * y^2
= 49*x^2*y^2
4). x^3 / x^2
= x
5). 7^0
=. 1
6). 8x^0
= 8
How many degrees was ABCD rotated?
Answers
the answer is 180°
Step-by-step explanation:
because it rotated 2x and 90+90 is 180
Find the slope of the line that passes through (1, -19) and (-2, -7)
Answers
Answer:
y = -4x-15
Step-by-step explanation:
y = ax+b
-19=a+b
-7=-2a+b
==> a = -4
b = -15
Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline.
Year, t 1960 1970 1980 1990 1995 1997 1998 1999
Gallons Consumed
Per Passenger Car 668 760 576 520 530 538 544 552
Determine the average rate of change, in gallons of gas per year, from 1960 to 1990.
a.
StartFraction delta g Over delta t EndFraction = 4.93 gal/year
b.
StartFraction delta g Over delta t EndFraction = negative 4.93 gal/year
c.
StartFraction delta t Over delta g EndFraction = 0.20 gal/year
d.
StartFraction delta t Over delta g EndFraction = negative 0.20 gal/year
Answers
Answer:
the answer is c
Step-by-step explanation:
On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4).
What is the rule for the reflection?
A. rx-axis(x, y) → (–x, y)
B. ry-axis(x, y) → (–x, y)
C. rx-axis(x, y) → (x, –y)
D. ry-axis(x, y) → (x, –y)
Answers
Answer:
B. Ry-axis(x, y) → (–x, y)Step-by-step explanation:
As per the graph we see that:
Reflection over y-axis, y- coordinates remain as is, x- coordinates change to oppositeSo the rule is:
Ry-axis (x, y) → ( - x, y)Correct option is B
Answer:
B. ry-axis(x, y) → (–x, y)
Step-by-step explanation:
Took the quiz, hope this helps! :)
Find the interest.
. 750$, 6.5%, 2years
Answers
Answer:
simple interest=$97.50.
compound interest= $100.668
Step-by-step explanation:
Given:
Principal (P) = $750
Rate (R) = 6.5% (in decimal form, 0.065)
Time (T) = 2 years
Simple Interest = Principal*Rate*Time
Using the formula, the simple interest is calculated as follows:
Simple Interest = $750*0.065*2 = $97.50
Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.
Again:
Compound Interest = Principal*(1 + Rate)^(Time)-Principal
Using the same values as above, the compound interest can be calculated as follows:
Compound Interest = $750*(1+0.065)^(2)-$750
= $750*1.065^2 -$750
= $750 × 1.134225 - $750
= $850.66875-$750
= $100.668
Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668
Mystery Boxes: Breakout Rooms
The boxes below contain 14 numbers, listed in order, of which 6 have been removed. Your job is
to use the clues given to determine the missing numbers. Write your answers in the boxes.
• The mean is 26
• The median is 22
The interquartile range is 20
The mode is 18
. The range is 60
1
4
15
18
29
30
32
58
Answers
Answer:
\(\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}\)
Step-by-step explanation:
Given
\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}\)
Required
Fill in the box
From the question, the range is:
\(Range = 60\)
Range is calculated as:
\(Range = Highest - Least\)
From the box, we have:
\(Least = 1\)
So:
\(60 = Highest - 1\)
\(Highest = 60 +1\)
\(Highest = 61\)
The box, becomes:
\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
From the question:
\(IQR = 20\) --- interquartile range
This is calculated as:
\(IQR = Q_3 - Q_1\)
\(Q_3\) is the median of the upper half while \(Q_1\) is the median of the lower half.
So, we need to split the given boxes into two equal halves (7 each)
Lower half:
\(\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}\)
Upper half
\(\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
The quartile is calculated by calculating the median for each of the above halves is calculated as:
\(Median = \frac{N + 1}{2}th\)
Where N = 7
So, we have:
\(Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th\)
So,
\(Q_3\) = 4th item of the upper halves
\(Q_1\)= 4th item of the lower halves
From the upper halves
\(\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
We have:
\(Q_3 = 32\)
\(Q_1\) can not be determined from the lower halves because the 4th item is missing.
So, we make use of:
\(IQR = Q_3 - Q_1\)
Where \(Q_3 = 32\) and \(IQR = 20\)
So:
\(20 = 32 - Q_1\)
\(Q_1 = 32 - 20\)
\(Q_1 = 12\)
So, the lower half becomes:
Lower half:
\(\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}\)
From this, the updated values of the box is:
\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
From the question, the median is:
\(Median = 22\) and \(N = 14\)
To calculate the median, we make use of:
\(Median = \frac{N + 1}{2}th\)
\(Median = \frac{14 + 1}{2}th\)
\(Median = \frac{15}{2}th\)
\(Median = 7.5th\)
This means that, the median is the average of the 7th and 8th items.
The 7th and 8th items are blanks.
However, from the question; the mode is:
\(Mode = 18\)
Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:
\(7th = 18\)
The 8th item is calculated as thus:
\(Median = \frac{1}{2}(7th + 8th)\)
\(22= \frac{1}{2}(18 + 8th)\)
Multiply through by 2
\(44 = 18 + 8th\)
\(8th = 44 - 18\)
\(8th = 26\)
The updated values of the box is:
\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
From the question.
\(Mean = 26\)
Mean is calculated as:
\(Mean = \frac{\sum x}{n}\)
So, we have:
\(26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}\)
Collect like terms
\(26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}\)
\(26= \frac{ 2nd + 12th+304}{14}\)
Multiply through by 14
\(14 * 26= 2nd + 12th+304\)
\(364= 2nd + 12th+304\)
This gives:
\(2nd + 12th = 364 - 304\)
\(2nd + 12th = 60\)
From the updated box,
\(\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}\)
We know that:
The 2nd value can only be either 2 or 3
The 12th value can take any of the range 33 to 57
Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:
\(2nd = 3\)
\(12th = 57\)
i.e.
\(2nd + 12th = 60\)
\(3 + 57 = 60\)
So, the complete box is:
\(\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}\)
h(t) = – 16t2 + 48t + 28
Answers
Answer:
-4(2t+1)(2t-7)
Step-by-step explanation:
First factor out the common term -4
Then factor out -4^2
Answer:
the answer is( -42t+1)(2t-7)
PLEASE HELP!!!!!!!
In comparison to the parent function f(x)=square root x,
When does a graph move up? When does a graph move down?
Answers
Answer:
Parent function:
f(x) = √x
Add a number to the value of the function, such as k:
f(x) = (√x) + k
If k is positive, the function moves up. If k is negative, the function moves down.
13
Use the drawing tools to form the correct answer on the graph.
Graph the composite function (f(x)).
f(x) = -2x- 5
g(x) =x - 1
Drawing Tools
Select
Point
Click on
Answers
The graph of the composition of functions is on the image at the end.
How to graph the composite function?Here we want to graph the composition of the functions g(x) and f(x), where:
f(x) = -2x - 5
g(x) = x - 1
The composition:
g(f(x)) will give:
g(f(x)) = f(x) - 1 = -2x - 5 - 1 = -2x - 6
So it is just a linear function, basically it is a translation of 1 unit down of f(X), the graph of this composition is on the image at the end.
Learn more about compositions at:
https://brainly.com/question/10687170
#SPJ1
I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
learn more on kite here: https://brainly.com/question/27975644
#SPJ9
A sum of money was distributed among some boys. Had there been two boys more, each would have received Rs. 10 less. Had there been two boys less, each would have received Rs. 15 more. Find the number of boys and the sum received by each.
Answers
Given -
A sum of money was distributed among some boys.Had there been two boys more, each would have received Rs. 10 less.Had there been two boys less, each would have received Rs. 15 more.To find -
the number of boys and the sum received by each.Explanation -
Here as we are required to find the value of two different individuals hence first we will from 2 linear equations into two variables (taking each to be value as x and y or whatever you like, I will take them as a and b) will solve the equation by any method of your choice (explanation for them is in the link, below, it is given by the same me)
https://brainly.com/question/27161912?utm_source=android&utm_medium=share&utm_campaign=question
Solution -
Let the sum of money that was given to each boy be a and the number of boys be b. Hence, the total no. of money distributed to b no. of boys is ab.
According to the question,
Scenario 1 -
➡ (a + 2)(b - 10) = ab
Solving it further,
➡ a(b - 10) + 2(b - 10)= ab
➡ ab - 10a + 2b - 20= ab
Cancelling ab,
➡ 10a - 2b + 20 = 0
➡ 10a = 2b - 20
➡ a = 2(b - 10)/10
➡ a = (b - 10)/5
Scenario 2 -
➡ (a - 2)(b + 15) = ab
Solving it further,
➡ a(b + 15) - 2(b + 15)= ab
➡ ab + 15a - 2b - 30= ab
Cancelling ab,
➡ 15a - 2b - 30 = 0
Substituting the value of a in the equation,
➡ 15{(b - 10)/5} - 2b - 30 = 0
➡ 3(b - 10) - 2b - 30 = 0
➡ 3b - 30 - 2b - 30 = 0
➡ 3b - 2b -60 = 0
➡ b = 60
Substituting the value of b in a = (b - 10)/5,
➡ a = (60 - 10)/5
➡ a = 50/5
➡ a = 10
[Here we have used the substitution method]
Henceforth, the total number of boys is 60 and the sum received by each is Rs. 10 .